1
2 /* @(#)k_sin.c 1.3 95/01/18 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16
17 /* __kernel_sin( x, y, iy)
18 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
19 * Input x is assumed to be bounded by ~pi/4 in magnitude.
20 * Input y is the tail of x.
21 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
22 *
23 * Algorithm
24 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
25 * 2. Callers must return sin(-0) = -0 without calling here since our
26 * odd polynomial is not evaluated in a way that preserves -0.
27 * Callers may do the optimization sin(x) ~ x for tiny x.
28 * 3. sin(x) is approximated by a polynomial of degree 13 on
29 * [0,pi/4]
30 * 3 13
31 * sin(x) ~ x + S1*x + ... + S6*x
32 * where
33 *
34 * |sin(x) 2 4 6 8 10 12 | -58
35 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
36 * | x |
37 *
38 * 4. sin(x+y) = sin(x) + sin'(x')*y
39 * ~ sin(x) + (1-x*x/2)*y
40 * For better accuracy, let
41 * 3 2 2 2 2
42 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
43 * then 3 2
44 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
45 */
46
47 #include "math.h"
48 #include "math_private.h"
49
50 static const double
51 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
52 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
53 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
54 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
55 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
56 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
57 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
58
59 double
__kernel_sin(double x,double y,int iy)60 __kernel_sin(double x, double y, int iy)
61 {
62 double z,r,v,w;
63
64 z = x*x;
65 w = z*z;
66 r = S2+z*(S3+z*S4) + z*w*(S5+z*S6);
67 v = z*x;
68 if(iy==0) return x+v*(S1+z*r);
69 else return x-((z*(half*y-v*r)-y)-v*S1);
70 }
71